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Cayley Tournaments Simultaneously Critical for the Clique and Dichromatic Numbers
For a tournament $T$, let $ω(T)$ be the minimum clique number among the backedge graphs of $T$, and let $χ(T)$ be its dichromatic number. We give a template-lifting construction. It turns a $k$-template into a regular, vertex-transitive Cayley tournament that is simultaneously $(k+1)$-$ω$-critical a
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